As the results show, our proposed method outperforms the previous algorithms in the three tasks; Mutagenesis, Cora and IMDB. In case of IMDB dataset, it reaches the perfect classification (AUROC=1.0, AUPR=1.0). This impressive performance is only made possible because of the ability of learning recursive predicates. Indeed, when we disallow the recursion in this model, the AUPR performance drops to \(0.76\) .
The end-to-end design of our differentiable ILP solver makes it possible to combine some other forms of learnable functions with the dNL networks. For example, while handling continuous data is usually difficult in most ILP solvers, we can directly learn some threshold values to create binary predicates from the continuous data (see Appendix )Alternatively, we can assign learnable probabilistic functions to those variables (see Appendix ).. We have used this method in the Mutagenesis task to handle the continuous data in this dataset. For the case of UW-CSE, however, our method did not perform as well.
One of the reasons is arguably the fact that the number of negative examples is significantly larger than the positive ones for this dataset.
Indeed, in some of the published reports, (e.g. [1]}), the number of negative examples are limited using the closed world assumption as [2]}. Because of the difference in hardware, it is difficult to directly compare the speed of algorithms. In our case, we have evaluated the models using a 3.70GHz CPU, 16GB RAM and GeForce GTX 1080TI graphic card. Using this setup the problems such as IMDB, Mutagenesis are learned in just a few seconds. For Cora, the model creation takes about one minute and the whole simulation for any fold takes less than 3 minutes.
